Course: Grade 10 Applied Math, Topic: Finding surface area

​After seeing Andrew Stadel's File Cabinet 3-Act Lesson, we thought it would be an easy one to do with our 10 applied classes near the beginning of the semester.  We didn't just want to watch the Andrew Stadel video though, we wanted our students to actually cover an iPad cart with post-its.  

​After going through the Andrew Stadel 3-Act lesson as a class, I put a few post-its on the cart.  After recording some initial estimates, they immediately got to work measuring and calculating...

"But it would take a whole period to cover the whole cart with post-its!  How on earth do you have time for that???" 
Not every student needed to be involved.  After a quick lesson on calculating surface area, I asked the 2 or 3 students who finished the surface area practice problems quickly or the students who were finding it too easy to do it.  As the rest of the class practiced calculating surface area, they stuck 'em on.  It did end up taking the better part of a period but those students were happy to do it! 
The anticipation in the class grew as more an more post-its were added.  It was super satisfying for everyone to get a final, definite answer (see video below).  It was also great to see the Grade 9's and 12's who came into the classroom afterwards spontaneously start asking questions about the post-it covered cart.  "Can we do more lessons like that too?" 

Covering the curriculum strand by strand, unit by unit is over.  At least for me.  Spiralling the curriculum gave me the flexibility I needed to have a successful semester with the students.  

Course Structure:
​The curriculum was covered in 4 cycles.  Each cycle had a theme.  Complexity increased as the course went on.

• Cycle 1 - Introduction to the types of functions (polynomial, exponential, sinusoidal)
• Cycle 2 - Modelling with functions (polynomial, exponential, sinusoidal)
• Cycle 3 - Solving equations (polynomial, exponential, sinusoidal)
• Cycle 4 - Vectors
• Sprinkled in each cycle were unit conversions and geometry

The cycles allowed me to come back to the different types of functions throughout the semester and be more flexible with the activities.  Students remembered material much better and enjoyed the constant changing of topics instead of focusing on one topic for a month.

Here is a link to my cycle plans for the semester.

Activity Structure:
Each cycle contained multiple activities.  An activity would last 3-6 days on average and would be structured as follows:

• Activity [1-2 days] - hands on to collect data, work through an investigation
• Lesson [1 day, half period] - explicit instruction formalizing the skills used in the activity
• Practice [1-3 days] - in-class problems in handouts (not too many, not too hard) followed by group problems they answered on white boards (as many as necessary for them to really get it) followed more in-class problems.  Practice problems were often collected as assignments to reward hard work and a good use of class time.
• Assess - short exit/entrance quiz for each topic (or multiple per topic), quiz after 1 or 2 activities, test at the end of the cycle.

I made the structure of the course clear to the students from the beginning of the semester.  They were totally on board with the idea of spiralling.  Some quotes when I explained it to them on the first day:
"This way makes so much sense!"
"Why don't all math courses work this way?"

This is the first semester I tried spiralling (in both MCT4C and MFM2P) and I'm sold.  Though it's daunting at first, I now think it is much more flexible to plan and a much more natural way to learn.